The president cannot declare war without the approval of Congress. As the commander in chief of the armed forces, however, the president has the power to send troops into battle without an official war declaration from Congress.
The War Powers Act of 1973 added strict time frames to report to Congress after sending troops to war in an attempt to define when the president was able to send troops to battle. A presidential executive order can be used in times of emergency with the power to override Congress. The president has the power to call into service the state units of the National Guard.